Jun 042012

Allosteric regulation of proteins is often examined using two different models. The widely-known “induced-fit” (IF) model proposes that effectors form a loose complex with inactive proteins and cause them to shift into a new, active conformation. In the competing “conformational selection” model, effectors bind to and stabilize proteins that are already in an active conformation. An upcoming paper in the Journal of the American Chemical Society examines this question in the case of T. lanuginosis lipase (TLL) (1). The data show that the enzyme enters an activated state even when it is prevented from interacting with its activator. While this strongly suggests that the activation mechanism is CS, some data suggest that the mechanism is actually IF.

The paper in question relies on single-molecule kinetics techniques to characterize an enzyme. Previous studies in this field have shown that reaction time varies between enzyme molecules and over time for single molecules. These findings should not surprise us, knowing as we do that all machines have intrinsic variation in their rates of operation. Flexible proteins that can adopt many different folded structures (not to mention partially-folded and unfolded ones) should be expected to have even more operational differences. That said, there are a variety of ways to account for the observed distribution of reaction rates.

TLL is activated by lipid membranes. While tracking the activity of individual enzymes using fluorescence, Hatzakis et al. altered their ability to access a lipid membrane by changing the concentration of polyethylene glycol (PEG) in the solution; PEG blocks the (tethered) enzyme from accessing the liposome. They found that a model where the enzyme exists in an equilibrium of active (R) and inactive (T) states is most consistent with the distribution of reaction times they observe, even at PEG levels that completely occlude the membrane. Based on this finding, they conclude that TLL activation occurs by selection of an active conformation from a pre-existing equilibrium, rather than inducing a new conformation.

At this point things start to get a little confusing. The central problem is that CS and IF are used to identify both characteristics of the apo- ensemble and features of the activation pathway, and the former don’t necessarily coincide with the latter.

To understand what I mean, take a look at the figure below. Here, Ta and Ra are ligand-free T and R states, while Tb and Rb are ligand-bound T and R states. The typical ligand-free state is Ta, and the allosterically activated state is Rb. Ra (apo-R state) and TbL (“encounter complex”) are thermodynamic states that are viewed as characteristic of CS (red path) and IF (blue path), respectively. The rates kact and kin are the apparent rates of activation and inactivation, which are dependent on the microscopic rates noted for each pathway.

Comparison of CS and IF mechanisms

In a CS mechanism, the protein adopts both the R and T structures while free in solution, and ligand binds preferentially to the R state and stabilizes it, redistributing this pre-existing equilibrium without creating “new” states. Because binding follows conformational change, a pre-existing equilibrium in the apo- ensemble is a necessary condition of CS.

In the IF case, binding precedes conformational change: the ligand encounters the free T structure and allows it to adopt a “new” R structure. Traditionally, this has been interpreted to mean that the R structure never exists in solution at all. However, binding may proceed by an induced-fit mechanism even if an R state is populated in solution.

There are a couple of cases where we know this must happen. For instance, adenylate kinase, a protein that I have discussed before, undergoes conformational exchange between open (T) and closed (R) states in solution. However, in the closed state the ligand-binding site is completely occluded, and it is impossible for ligands to bind to this state. It therefore follows that binding-associated conformational change proceeds by an IF-like pathway, even though an equilibrium between the R and T structures exists in the apo- state. In this and similar cases, all four major states are populated, but kon,R≈0 and so the path through TbL dominates the reaction flux.

The thermodynamic implication of CS — that there is a detectable equilibrium between R and T states — is not synonymous with its mechanistic meaning — that conformational change precedes binding. This makes sense, because in the context of a constantly interconverting ensemble of conformations, even very unfavorable Ra states will be accessed occasionally. The strict thermodynamic definition of IF, that the R conformation be unattainable in the apo- state, may not apply to any real protein (2). However, the population of R conformers may be so low and short-lived as to be undetectable.

Even though a pre-existing equilibrium is not probative, a quick examination of the figure above indicates how we can distinguish between these mechanisms. In the case of CS, the rate of interconversion between T and R states in solution sets an upper limit on the activation rate, because the ligand binds to the apo-R state. At high ligand concentrations, kact = kTR because the presence of ligand probably will not alter the energy landscape of a protein it is not bound to. In this mechanism, however, koff,R is expected to be much slower than kRT. This implies that kin should decrease significantly at high ligand concentrations.

In an IF mechanism, the energy landscape of the encounter complex need not be the same as that of the apo- protein. As such, in IF activation the T→R energy barrier can (and is expected to) become lower. Accordingly, if kact exceeds kTR at high ligand concentrations (3), then an IF mechanism must be at work. Because this energy barrier is variable in an IF mechanism, however, it’s somewhat difficult to predict what will happen with the R→T barrier; it might get larger, or it might not. The figure below summarizes the expectations.

Hatzakis et al. report that the rate of conversion from T to R (i.e. kact) increases as PEG concentration decreases (note: in the advance online version the schemes in Figures 2 and 4 are mislabeled, but the energy diagram in 4 is accurate). The kin rate, by contrast, remains constant. If we accept their (reasonable) assumption that the energy of Ta is not affected by the lipid membrane, this indicates that the T→R energy barrier decreases in the presence of the allosteric effector. That, in turn, implies that the membrane is associated with the protein prior to the transition state, and thus that the mechanism of activation is induced fit, even though an Ra state can be observed in solution.

“Conformational selection” is often used interchangeably with “pre-existing equilibrium”, but it is dangerous to employ this equivalence. The thermodynamic feature of a pre-existing equilibrium between apo -inactive and -active states does not necessarily imply that the pathway between apo-inactive and bound-active states proceeds through an apo-active intermediate. In some cases, the observed equilibrium indicates a kinetic dead-end where kon,R≈0 and the reaction flux is dominated by IF mechanisms.

Hatzakis et al. studied the single-molecule kinetics of several other allosterically-regulated monomeric enzymes and found that they also showed evidence of a pre-existing equilibrium between active and inactive states. This alone, however, is not sufficient to establish activation via CS. Only a detailed examination of the kinetics can indicate whether activation uses CS, IF, or some combination of these mechanisms.

1) Hatzakis, N., Wei, L., Jorgensen, S., Kunding, A., Bolinger, P., Ehrlich, N., Makarov, I., Skjot, M., Svendsen, A., Hedegård, P., & Stamou, D. (2012). Single Enzyme Studies Reveal the Existence of Discrete Functional States for Monomeric Enzymes and How They Are “Selected” upon Allosteric Regulation Journal of the American Chemical Society DOI: 10.1021/ja3011429

2) By the same token, apo-R states are almost certainly not exactly the same as bound-R states, so a strict version of CS is also quite improbable.

3) At substoichiometric concentrations of ligand, kact can exceed kTR because in this condition maximum activation can be reached by (rapid) binding of ligand to the existing pool of Ra, without any need to replenish Ra from Ta.

Sep 062011

Over the last two decades, multiple kinds of NMR experiments have repeatedly shown that protein structures are quite variable, frequently shifting to minor conformations. The most striking evidence in this line has come from hydrogen-exchange experiments, which have demonstrated that virtually all proteins undergo excursions to partially-folded states at equilibrium. As R2 relaxation-dispersion experiments have become more widely used, excursions to alternative folded states have repeatedly been detected. The challenge now is to find ways to characterize these low-population states. Advanced crystallographic techniques have proven useful in determining some of these alternative structures. However, proteins are not always amenable to crystallography, and the minor state in the crystal may not correspond exactly to the minor state in solution. Therefore there is an ongoing effort to define these states by NMR. Lewis Kay’s group in Toronto is in the forefront of this effort, and recently reported the solution structure of a minor state of a T4 lysozyme mutant (1).

Lysozyme is an extremely common enzyme because it has the useful property of degrading the peptidoglycan that makes up bacterial cell walls. This makes it a natural antibiotic against gram-positive bacteria, and as a result it is found in many secretions and fluids, including saliva and egg whites. Because it is plentiful it has been widely studied, with many mutants made and characterized for their activity and stability. Lysozyme also crystallizes easily — doing this was actually part of my biochemistry lab class back in college. So, many structures of the enzyme and its mutants are available.

T4 lysozyme L99A with benzene boundOne lysozyme mutant that has interesting properties is the L99A mutant of the lysozyme from the T4 bacteriophage. This mutation creates a cavity in the upper part of the protein that is known to bind hydrophobic ligands such as benzene (right, benzene in purple, PDB code 3DMX). However, crystal structures show this binding pocket to be completely buried, even when empty. This poses the question of how the ligand gets in. Although the structure of L99A is very similar to WT, the Kay lab noticed that the NMR spectra of the mutant contained broadened peaks, indicating the presence of an exchange process between two conformations. Therefore, the Kay lab used R2 relaxation-dispersion to show that the protein sampled a minor state that accounted for 3% of the total protein, with a lifetime of about 1 ms (2). This conformation was presumed to be the binding-competent form of the protein. However, without a structure of this state, they could not confirm that the pocket was accessible. This led to their present attempts to characterize this low-population state using NMR.

As I have mentioned before, R2 relaxation-dispersion experiments can provide three important pieces of information: the populations of the two conformational states (pG, pE for ‘Ground’ and ‘Excited’), the rate of exchange between them (kEX = kGE + kEG), and the difference in chemical shift between the two states at each nucleus (|Δω|). Because the chemical shift is determined by the protein conformation, and because additional experiments can determine the sign of Δω, it should be possible to figure out the structure of the alternate state, given enough relaxation-dispersion data. Therefore, the Kay lab performed a large number of experiments to determine Δω for nearly all of the backbone 15N, 13C, and 1H atoms, as well as many side-chain methyl groups. They then fed this data to the CS-ROSETTA protocol, which can determine a protein structure using chemical shifts alone. While holding the majority of the protein in a single conformation, they allowed CS-ROSETTA to remodel the part of the mutant where they had detected conformational fluctuations.

Lysozyme minor state/major state overlay
Major state (green) and 5 lowest-energy conformers of the minor state (Excited) ensemble (blue)

Using this method, they were able to produce a structure of the transiently-populated minor state of the mutant protein, which I show to the left in comparison to the major conformation (PDB codes 2LCB and 3DMV, respectively, aligned using residues 10-100, 150-160). The most dramatic change is that two of the helices have been fused into one. As you can see, the new helix clashes with the usual position of phenylalanine 114 (pale green, because of the overlap it’s hard to see), which has in turn shifted so that it occupies part of the cavity where benzene binds (pale blue). This suggests, contra the Kay group’s earlier work, that the minor state is also incapable of binding to benzene.

This is a difficult prediction to test in the L99A system because the minor state (E) lives for such a short time that it’s difficult to tell whether anything binds to it or not. Therefore, Bouvignies et al. made a double-mutant protein with the L99A mutation and an additional G113A mutation that was predicted to stabilize the long helix observed in the minor form. This turned out to be the case: the E structure was enriched in the double mutant. In addition, the interconversion rate was slow enough that at low temperature distinct peaks could be observed for each conformation, as well as cross-peaks indicating exchange between them (I discussed this kind of experiment in my previous posts about cyclophilin). Under these conditions, the minor form is sufficiently populous and long-lived to determine whether ligands bind to it.

The Kay group did this by adding an equimolar amount of benzene to the reaction and observing whether there were exchange peaks. If you examine their figure 3c, it’s clear that exchange occurs between all three possible states: (G)round, (E)xcited, and (B)ound. This might seem to contradict their hypothesis. However, the E→B exchange peaks have very low intensity and take significantly longer to reach a maximum than the other exchange peaks. Therefore, this exchange peak may represent a low-frequency E→G→B event rather than direct exchange between the E and B states. Fits of the exchange curves seem to substantiate this interpretation, as the fit tended towards a value of zero for kEB and the χ2 jumped up significantly when kEB was fixed to a very low number.

My only concern with this result is that the kEG rate changes from ~31 to ~36 s-1 when benzene is added (kGE remains the same). It’s possible that the presence of benzene really does accelerate this process, or that the errors are underestimated. The model might also be janky in some hidden way, but my back-of-the-envelope check of the parameters suggests that the results are consistent with what is known about benzene binding to the L99A mutant, e.g. various ways of calculating the KD from these data produce a value of approximately 1 mM, matching earlier results.

If the E state does not represent a binding-competent state, that means the protein must be exchanging to yet another, still-undetected state. According to Bouviginies et al., the E structure they determined can account for all of the observed chemical exchange. If the alternative state that is capable of admitting benzene to the hydrophobic pocket cannot be detected by relaxation-dispersion experiments, it must constitute a very small fraction of the overall protein population (< 1%) and undergo very fast exchange. In principle, the existence of such a process can be detected using experiments designed to measure the intrinsic R2 of a residue, and also should be detectable using 1H experiments directed towards the methyl groups (the side chains likely represent the best bet for explaining the phenomenon). It does not appear that those experiments have been done yet, but I’m certain they’re underway.

Bouvignies et al. made a third construct incorporating the R119P mutation to stabilize the E state even further. This succeeded, producing a protein that spent most of its time in the E state and occasionally sampled the G state. The paper contains no data as to whether benzene detectably binds this mutant, although that strikes me as an obvious experiment to try. Presumably the obligate route through a high-energy intermediate would slow the kinetics of binding relative to the single mutant. If the penalty for adopting the G fold in this mutant is high enough, it might also significantly reduce the affinity.

The findings in this paper are not of any immediate practical use. The L99A mutant is a biophysical curiosity, not a disease target, and most of these techniques have been presented before, at least individually. However, this does serve as a very nice example of the advanced NMR methods that allow the determination of minor states, and of the surprising findings that can be derived from them. This paper should serve as a model approach to this sort of question, which may find broad applicability in the study of signaling, ligand binding, and protein evolution.

Disclaimer: I am currently collaborating with David Baker’s lab on a research project using ROSETTA.

1) Bouvignies G, Vallurupalli P, Hansen D, Correia B, Lange O, Bah A, Vernon R, Dahlquist FW, Baker D, & Kay LE (2011). Solution structure of a minor and transiently formed state of a T4 lysozyme mutant Nature, 477 (7362), 111-114 DOI: 10.1038/nature10349

2) Mulder FA, Mittermaier A, Hon B, Dahlquist FW, & Kay LE (2001). Studying excited states of proteins by NMR spectroscopy. Nature structural biology, 8 (11), 932-5 PMID: 11685237

Dec 022010

ResearchBlogging.orgIn the Monod-Wyman-Changeux model for cooperative binding, proteins exist in an equilibrium of low-affinity and high-affinity states in solution, absent any ligand. In this view, although it may appear that the binding of a ligand causes a conformational transition, it actually stabilizes one conformation from a pre-existing equilibrium. In the past several years, advanced NMR techniques have yielded increasing evidence that these structural equilibria exist for a number of proteins, suggesting that this model for linkage between conformational change and binding may be quite general. An upcoming paper in the Journal of Molecular Biology (1) is typical of such findings.

Farber and Mittermaier studied the behavior of a homeodomain, a small, all-helical domain that typically binds to DNA, often in concert with other homeodomains. In particular, they were interested in the homeodomain of PBX1 (PBX-HD) which binds DNA cooperatively with a homeodomain from HOXB1 (HOX-HD). The domains interact with the DNA target and with each other. Peptides representing the binding site from the HOX-HD bind detectably to PBX-HD only in the presence of the target DNA, suggesting that the two binding sites communicate. The third helix of the PBX-HD is likely to mediate the allostery since it’s involved in both binding interactions, but it’s not clear from the available structures how this would happen. Additionally, there is a C-terminal sequence, with no defined fold in the free structure, that forms a helix in the ternary complex. It does not interact directly with the DNA, but removal of this extension decreases the affinity of PBX-HD for DNA and weakens the cooperativity between PBX-HD and HOX-HD.

Helix folding has a low energy barrier, so it is reasonable to suspect that this helix could form even in the absence of DNA. Farber and Mittermaier examined this possibility using a technique I have often discussed on this blog: CPMG relaxation dispersion. As you may recall, this technique is sensitive to fluctuations between states (chemical exchange) that persist for microseconds or milliseconds. One can in principle determine the rate of exchange (kex), the population of each state (pA, pB), and the chemical shift difference (|Δω|) between them, although if the motion is too fast or too slow only composites of some of these can be reliably determined. When they performed the experiment, the authors found that residues throughout PBX-HD had significant broadening, indicating chemical exchange and suggesting that the protein does not spend all its time in one folded state. The relaxation-dispersion profiles they obtained at 10 °C and 15 °C were in the intermediate regime, where all three of the aforementioned parameters can be determined.

For the C-terminal extension, the |Δω| determined by fitting the relaxation-dispersion data were linearly correlated with the chemical shift change that was observed in an HSQC upon binding (|Δδ|). The correspondence wasn’t exactly 1:1, but this is still reasonably good evidence that the helix is folding independent of binding. The authors used the |Δω| from the 10 °C fits to pull populations and rates from the experiments performed at higher temperatures, where only a composite parameter can be reliably determined (due to the speed of the fluctuation). Arrhenius plots derived from these data indicate thermodynamic parameters that are consistent with the folding of a single helix, again supporting the proposition that the C-terminal helix can fold on its own.

Numerous residues in the folded portion of the domain also experienced chemical exchange, which could mean that the helix is not the only thing undergoing a structural transition. The authors fit these residues individually, then tried again while fixing kex to the value determined from the helix behavior. The latter fits were not much worse in terms of their residuals than the floating fits were, so the fluctuations here could reasonably be seen as consistent with the helix-folding fluctuation.

If this is so, then removing this unstable helix should quench the dynamics in the folded part of the protein. This turned out to be the case — when the helix was removed, the dispersion curves for residues in the folded part of the protein became flat. This reinforces the case that the dynamics detected in the folded domain are related to the folding of the helix, and therefore represent an excursion to the “bound” structure for ligand-free protein.

Farber and Mittermaier note that for residues in the folded portion of the domain, the |Δω| determined through the CPMG analysis does not appear to agree with the |Δδ| observed upon binding DNA. From this they conclude that the conformational change in solution is actually going to some unknown third state that is different from both the free and bound structures. I disagree somewhat with this interpretation. Because the ligand (in this case a piece of double-stranded DNA) is large relative to the protein and possesses substantial negative charge, there’s a significant possibility of long-range electrostatic effects on the chemical shift of the PBX-HD. That is, the protein’s bound state might have different chemical shifts free in solution and bound to the ligand even without any major conformational changes. If this is the case, the |Δω| will correlate best with |Δδ| for residues that are far from the interface. Probably the structure sampled by the free protein is not exactly the same as the bound structure, but I think further data would be needed to determine whether the alternative structure in the free state differs significantly from the bound structure with DNA.

The uncertainty about the alternative structural state of the free protein makes it more difficult to make a firm argument about whether the binding mechanism more closely resembles conformational selection or induced fit, or whether it’s some kind of middle ground between the two. Although it’s suggestive, the observation of a structural equilibrium in the free state does not actually indicate how binding occurs. Moreover, because this is a complicated ternary complex, it is possible that, say, the protein-binding mechanism is conformational selection, while the DNA mechanism is induced-fit. This latter possibility might seem more sensible in light of existing studies indicating that long-range (e.g. electrostatic) interactions may predispose a system to induced-fit binding.

Complications aside, these data seem to support a model in which the PBX-HD transiently adopts the bound conformation in the absence of ligand. Binding of the PBX-HD domain to DNA shifts its population towards the state that is the minority in solution. This new structure has high affinity for the HOX-HD, promoting the formation of the ternary complex. In principle, binding of the HOX-HD to PBX-HD could precede DNA binding by both modules, but the interaction between these proteins appears to be weak in the absence of DNA. However, proving that the excursion to the bound (or near-bound) PBX-HD structure represents an actual intermediate in the binding process rather than  just an interesting fluctuation on the side will require some determination of the binding kinetics in various conditions.

(1) Farber, P., & Mittermaier, A. (2010). Concerted Dynamics Link Allosteric Sites in the PBX Homeodomain Journal of Molecular Biology DOI: 10.1016/j.jmb.2010.11.016

Aug 082008
ResearchBlogging.orgThe binding of a ligand to a protein rarely occurs with the simplicity of a block sliding into an appropriately-shaped hole. Protein and ligand often engage in complementary conformational changes to adapt their shapes to each other. As a result, the structure of a protein bound to its target may differ substantially from the structure of the free protein. Unfortunately, it is virtually impossible to view the binding process in fine structural detail; as a result, most of our knowledge comes from the relatively stable bound and free states. Improving biophysical techniques, however, have brought a change in the way we view some binding events.

Most alterations of conformation during a binding event have historically been interpreted using the induced fit model. In this view, the protein stably maintains the free or “open” structure until it comes into contact with a ligand molecule. This encounter stimulates a conformational change so that the protein adopts the “closed” conformation that tightly holds onto the ligand. Thus, the ligand induces the conformational change necessary to form the bound, closed (BC) structure from the unbound, open (UO) structure, and the intermediate on this path is some kind of bound, open (BO) structure. This model is physically reasonable and has been very successful in interpreting many systems.

However, for the past few decades an increasing amount of evidence has suggested that this is not the whole story. NMR investigations indicated that instead of remaining in a single, well-defined backbone conformation most of the time, many proteins experienced significant changes in their structure while floating free in solution. These results suggested an alternative mechanism of population shift. In this view, the protein actually samples the “closed” conformation (or something very similar) while unbound, and it is this conformation that binds to the ligand. We still go from UO to BC, but now the intermediate is an unbound, closed (UC) structure.

This sounds very arcane, but it is not without functional relevance. Consider, for instance, a protein that is activated by a particular ligand. If we wish to make a drug that binds exclusively to the BC form, then we may experience unforeseen side-effects if our target protein occasionally samples a UC state. It would be useful to have a general idea of what kinds of circumstances are likely to favor a population shift model vs. an induced fit model. That is precisely what Kei-Ichi Okazaki and Shoji Takada aim to provide in an upcoming paper in Proceedings of the National Academy of Sciences (1).

Okazaki and Takada performed a coarse-grained molecular dynamics simulation of glutamine binding protein. In the bound and unbound states they employed a double-well Gō model, a simplified representation of molecular forces, to represent “opening” and “closing”. To switch between these states (i.e. to represent binding) they used a Monte Carlo algorithm. This approach has the advantage of being quick and relatively inexpensive from a computational standpoint, but the results must be interpreted cautiously because the physics of the model are greatly simplified. They observe UO ↔ UC and UC ↔ BC events in this system, but they also observe UO ↔ BO and BO ↔ BC events. This suggests that the simulation will be able to make predictions about both population-shift and induced-fit mechanisms.

In order to try to make some predictions about the circumstances in which a particular mechanism is favored, Okazaki and Takada varied the strength and range of the binding interaction. By monitoring whether the simulated system entered the BC state from BO or UC, they could tell whether the system obeyed the induced-fit or population-shift mechanisms, respectively. They find that as either the strength or the range increase, the induced-fit mechanism is increasingly favored (Figure 4). These results make sense. If the protein regularly samples the closed state while unbound, then the amount of energy needed to reach that state is probably small, so it makes sense to see a population-shift mechanism associated with low-energy binding. Similarly, if a ligand is to associate productively with a non-optimal protein conformation, it makes sense that key interactions will be effective at long range.

From these results Okazaki and Takada suggest that the binding of small hydrophobic ligands is generally likely to proceed via population shift, while the binding of large, charged ligands (such as DNA) will likely proceed via induced fit. They acknowledge, however, that the simulation is limited, particularly in its view of conformational change. Unitary transitions in which the whole protein changes its structure simultaneously are probably not the norm, particularly in the case of very large conformational changes. These changes may instead be stepwise or hierarchical. For instance, a protein or complex recognizing multiple features of a DNA strand may proceed by an apparently induced-fit mechanism, even though each individual binding event more closely resembles population-shift behavior.

An additional limitation of this study is that it considers only one protein, but mechanisms of binding and conformational change may be idiosyncratic properties of particular folds. One could consider the behavior of lymphotactin, which displays clear hallmarks of the population-shift mechanism despite binding to macromolecules (heparin and a GPCR) much larger than itself, as a counterpoint to the predictions developed here. Similarly, the population shift of NtrC involves a charged phosphate group likely to have long-range interactions, although this is a post-translational modification and not a strict ligand-binding event. While the authors point to some examples that match their expectations, overall the data are not unanimously in support of their predictions. Still, the general rules laid out here provide a starting point for experimental work.

Despite the limitations of the simulation, it provides a relatively efficient tool for assessing these processes in other proteins. While no simulation can yet replace experimental data, coarse-grained models like this can serve as a means to formulate testable hypotheses about the energetics of protein-ligand systems.

1. Okazaki, K., Takada, S. (2008). Dynamic energy landscape view of coupled binding and protein conformational change: Induced-fit versus population-shift mechanisms. Proceedings of the National Academy of Sciences 105(32) 11182-11187. DOI: 10.1073/pnas.0802524105